Phylogenetically aligned component analysis

Abstract

1. It has become common in evolutionary biology to characterize phenotypes multivariately. However, visualizing macroevolutionary trends in multivariate datasets requires appropriate ordination methods. 2. In this paper we describe phylogenetically aligned component analysis (PACA): a new ordination approach that aligns phenotypic data with phylogenetic signal. Unlike phylogenetic PCA (Phy-PCA), which finds an alignment of a principal eigenvector that is independent of phylogenetic signal, PACA maximizes variation in directions that describe phylogenetic signal, while simultaneously preserving the Euclidean distances among observations in the data space. 3. We demonstrate with simulated and empirical examples that with PACA, it is possible to visualize the trend of phylogenetic signal in multivariate data spaces, irrespective of other signals in the data. In conjunction with Phy-PCA, one can visualize both phylogenetic signal and trends in data independent of phylogenetic signal. 4. PACA can distinguish between weak phylogenetic signals and strong signals concentrated in only a portion of all data dimensions. We provide empirical examples that emphasize the difference. Use of PACA in studies focused on phylogenetic signal should enable much more precise description of the phylogenetic signal, as a result. 5. Overall, PACA will return a projection that shows the most phylogenetic signal in the first few components, irrespective of other signals in the data. By comparing Phy-PCA and PACA results, one may glean the relative importance of phylogenetic and other (ecological) signals in the data.